The Virginia General Assembly may be the "oldest continuous law-making body in the New World" dating back to 1619 and the initial meeting of the House of Burgesses - but Prince William County was not created until 1731 (1730, Old Style). So this list does not include those officials who represented the area of Prince William County when it was part of Stafford and King George counties.
In the colonial era, Burgesses were the only officials elected directly by the voters in Prince William County. Local residents did not vote for their county court justices, who performed duties roughly equivalent to a combination of today's Board of County Supervisors and local judges. Those justices were appointed by the colonial governor, with all replacements appointed upon the recommendation of the current justices. And the sheriff was elected by those justices, not directly by the county residents who paid the taxes the sheriff collected. (Actually, there was one other election. When a new Anglican parish was created, there was one election for the initial members. After that, the vacancies were replaced by the remaining members of the vestry, not by the general population.)
Not everyone could vote, either - you had to be a white male over 21 years old with a certain level of property (typically 100 acres, or a lot in town with a house). Remember, when Prince William County was formed, the only republic known to the Virginians was the Roman republic from before the time of Christ. The English system of representative government was not "one person-one vote" back then, and many citizens in England never voted for a Member of Parliament either.
Elections occurred whenever the colonial governor called them, not on a scheduled basis. Newly-appointed governors would routinely call for new elections when they arrived in Virginia, to start with a new House of Burgesses. (Prince William was created when Governor Gooch was in office. He was later succeeded by governors Dinwiddie, Fauquier, Botetourt, and Dunmore before the Revolution and the selection of Patrick Henry as the first governor after independence.)
Elections would also be necessary after the governor dismissed the current House of Burgesses, often in frustration at the unwillingness of the House to vote as desired. It was illegal to campaign for office, and in the 1700's Virginia elections were usually not competitions between parties or even issues. Instead, they were opportunities to select a neighbor whose character was respected and who was trusted to represent the concerns of the local residents.
Candidates "stood" for election, rather than "ran" for office. It was bad form to request a vote directly, though it was permitted to have friends encourage others to vote. Candidates provided food and drink (especially alcohol) at the courthouse on election day for all voters, not just their friends. Election days provided excitement at the county courthouse, with individuals calling out their votes publicly and receiving equally-loud thanks from the candidates standing at the poll table. Usually 2, 3, or sometimes 4 or more candidates would "stand a poll," and two Burgesses would be selected from the county.
Prince William has an unusual history for its elections to the dozen House of Burgesses that sat between the formation of the county and the American Revolution. A surprisingly-high number of Prince William elections were competitions between bitter rivals, and several were declared void by the House of Burgesses. (The House jealously protected control over who could sit in it. If the House had been lax, there was a real possibility that the royal government would have maneuvered to have its own friends elected, eliminating any balance of powers and giving the King unlimited control over the colonists.)